1. When you apply a temperature Boundary Condition to the edges of a block of material, that is a fixed value that is enforced during the solution for all time. If you start with an object at 22 C at time = 0 and have four edges at 37 C and an internal heat generation, the block of material is only going to heat up. The maximum temperature in the block is only going to increase and never decrease. Why do you think it would decrease?

2. I put Convection on one edge to demonstrate a common Boundary Condition.